Metal–organic frameworks (MOFs) have been postulated for years as industrially achievable materials for CO2 capture and H2 storage. However, a great leap forward their real applications is still pending. This article details the design of a MOF material, including the reasoned choices of metal ion, organic linker, and even the structural subunits, as efficient adsorbent of both CO2 and H2. In particular, it was planned (i) to raise the polarizability of the framework by using a highly N-rich organic linker and (ii) to favor the formation of nanocavities with suitable size to confine small molecules. The resultant tetrazole-imidazole-based ITF-1 material containing nanocubes certainly achieved all these aimed premises. Nevertheless, such structural and compositional distinctiveness was reflected in some noteworthy adsorption features. CO2 adsorption was highly remarkable, and it was characterized by a wide hysteresis loop along the whole studied range of pressures. H2 molecules totally filled the nanocavities under only 0.1 bar at 77 K, and at 273 K, H2 uptake became tens of times higher than expected according to their textural properties. These unique adsorption results, together with the discussed relationship between structure/composition of ITF-1 and their adsorption features, underline the importance of a tailored MOF materials for particular applications.